Credit scoring involves assigning a risk score to a credit application or to an existing credit account based upon gathered data containing information related to a number of predictive variables. Before a predictive variable is used in a scorecard, it may be pre-processed to simplify the scorecard's predictive model using a variable transformation called “binning” (or “classing”). Binning maps the value range of a variable to a set of bins. A bin can comprise a single value, a finite set of values, a continuous range of values, or a missing value. After the scores are associated with determined bins, consumer data is applied to the developed scoring formulas for determining the creditworthiness of a particular scoring subject.
As described above, the model generation process includes a binning phase. In this phase, attributes (e.g. age, income, etc.) are segmented into grouping intervals, with the aim of aggregating a ‘weight of evidence’ (WOE) of a population into a small number of discrete bins. The WOE is typically the ratio of the normalized count of attribute sample members marked as good to those marked as bad. A typical credit-scoring practice is to take the logarithm of this value:
                    WeightOfEvidence        attribute            =              log        ⁢                              p            attribute            good                                p            attribute            bad                                ,                  ⁢    where              p      attribute      good        =                  #        ⁢                                  ⁢                  goods          attribute                            #        ⁢                                  ⁢        goods                        p      attribute      bad        =                  #        ⁢                                  ⁢                  bads          attribute                            #        ⁢                                  ⁢        bads            An optimal set of bins offers the highest predictive power by approximating the WOE of the binned model to the true WOE. Sometimes, bins are selected such that the resulting WOE can be approximated by a simple monotonic function. However, the desired function may also be of a more arbitrary shape. This process includes the enforcement of various constraints, such as minimum/maximum number of bins, minimum/maximum bin widths, maximum number of observations per bin, etc. These requirements significantly complicate the binning process because they involve the solution of nonlinear problems, ruling out the use of fully-enumerative methodologies.
Most existing algorithms solve this problem by starting with a discretization of the attribute variable in the form of fine bins that are heuristically combined to form larger aggregate (coarse) bins. This process has been traditionally done with no acknowledgement of the global structure, and thus sometimes fails to give solutions that satisfy globally defined constraints, such as monotonicity of WOE or maximum number of points per bin, and often fails to compute an optimal solution.